Note 7 — The Relation of Brightness to Mass

For this prediction it is unnecessary to know the chemical composition of the stars, provided that extreme cases (e. g. an excessive proportion of hydrogen) are excluded. For example, consider the hypotheses that Capella is made respectively of (a) iron, (b) gold. According to theory the opacity of a star made of the heavier element would be 2½ times the opacity of a star made of iron. This by itself would make the golden star a magnitude (= 2½ times) fainter. But the temperature is raised by the substitution; and although, as explained on p. 23, the change is not very great, it increases the outflow of heat approximately 2½ times. The resultant effect on the brightness is practically no change. Whilst this independence of chemical constitution is satisfactory in regard to definiteness of the results, it makes the discrepant factor 10 particularly difficult to explain.